Last week I filmed an event in a building that was so big and echoey that it sounded like being in an airport or something, the constant background noise making it hard to hear what the speakers were saying. Is there some procedure that as a general rule would be good for toning down that kind of background noise without cutting the quality of the speakers' voices as well?

At this point I have zero experience with audio FX other than editing volume envelopes, so the more spelled-out any advice would be the better!